In order to validate our model, we first calculated TE properties of SLG, using electronic band structure obtained from first principles in our previous work [1]}. Scattering rates are calculated using Eq. REF  and Eq. REF  with D\(_{ac}\)  = 3 eV, D\(_{op}^\Gamma \)  = 100 eV nm\(^{-1}\)  at \(\Gamma \) -point, and D\(_{op}^K\)  = 200 eV nm\(^{-1}\)  at K-point. The deformation potentials are taken from [2]} and adjusted to match the Seebeck coefficient [3]} and maximum power factor [4]} from the literature. The inelastic optical phonon processes are calculated at optical phonon energies of \(\omega _{op}^\Gamma \)  = 1589 cm\(^{-1}\)  = 0.197 eV at \(\Gamma \) -point and \(\omega _{op}^K\)  = 1197 cm\(^{-1}\)  = 0.148 eV at K-point taken from Ref. [5]}. Fig. REF (a) shows the \(S_{eff}\)  calculated for SLG at different temperatures by varying the carrier densities using Rode’s method. Our \(S_{eff}\)  and \(\sigma _{eff}\)  (Fig.REF ) for SLG are in agreement with measurements on hBN-encapsulated samples [4]}, [7]}. However, scattering from charged impurities in the environment can impact transport, lowering conductivity but raising the Seebeck [8]}. We neglect impurities here as their location and concentration varies from sample to sample depending on preparation conditions. A peak PF of 28.6 mW m\(^{-1}\)  K\(^2\)  is observed in SLG for electrons and 30 mW m\(^{-1}\)  K\(^2\)  for holes at 300 K in Fig.REF (c) when electric field is applied in [0 1] direction, in good agreement with measurements [3]}, [7]}, confirming the need to include the contribution from inelastic processes [11]}.
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